A park has 2 flagpoles 20m apart. One pole is 12m high and the other is 27m high. Calculate the angle of depression from the top of the taller pole to the top of the shorter pole. Round off your answer to the nearest hundredth.
PS. Please put an illustration/drawing of the problem. Thank you!
Answers
Answer:
37°
Step-by-step explanation:
Here it is given that there are two flagpoles which are 20 m apart. One of them is 12m high and the other is 27m high .And we are interested in finding the angle of depression from the top of taller pole to the top of shorter pole .
For illustration, refer to the attachment or below ,
Illustration :-
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(0,1){6}}\put(0,0){\line(1,0){4}}\put(4,0){\line(0,1){4}}\multiput(0,4)(0.6,0){7}{\qbezier(0,0)(0,0)(0.5,0)}\qbezier(0,6)(0,6)(4,4)\put(0,6){\vector(1,0){3}}\qbezier(0.8,6)(1,5.8)(0.6,5.7)\put(1,5.6){$\theta$}\qbezier(3.2,4.42)(3,4.1)(3.25,4)\put(2.4,4.15){$\theta$}\put(-0.5,-0.5){A}\put(-0.5,6){E}\put(-0.5,3.8){D}\put(-0.8,5){15m}\put(4.3,-0.5){B}\put(-1.2,2){$ 27m $}\put(3.2,6){$ F $}\put(4.5,2){$ 12m $}\put(4.3,3.8){C}\put(-1,1.8){\vector(0,-1){1.8}}\put(-1,2.4){\vector(0,1){3.7}}\put(2,-0.5){$ 20m$}\put(2,3.5){$ 20m$}\end{picture} [/tex]
Here the angle of depression will be ,
[tex]\longrightarrow\sf \angle_{of \ depression}=\angle FEC [/tex]
Also ,
[tex]\sf\longrightarrow \angle FEC =\angle ECD \ (alternate \ interior \ angles)[/tex]
Let ,
[tex]\sf\longrightarrow \angle FEC =\angle ECD = \theta \ ( say ) [/tex]
Now in ∆ EDC , we have;
[tex]\sf\longrightarrow tan\theta =\dfrac{perpendicular}{base}\\ [/tex]
[tex]\sf\longrightarrow tan\theta =\dfrac{15m}{20m}\\[/tex]
[tex]\sf\longrightarrow tan\theta =\dfrac{3}{4}\\ [/tex]
[tex]\sf\longrightarrow \theta =tan^{-1}\bigg\lgroup \dfrac{3}{4}\bigg\rgroup\\ [/tex]
[tex]\sf\longrightarrow \underline{\boxed{\textsf{\textbf{$\boldsymbol{\theta}$= 37$^{\bf o }$ }}}} [/tex]
And we are done!
Answer:
θ = 37°
Step-by-step explanation:
In the figure,
Distance between the poles = DC = 20 m
Height of the smaller pole = ED = 12 m
Height of the larger pole = AC = 27 m
Now, by using the properties of a rectangle,
DC = EB = 20 m
ED = BC = 12 m
Then,
AB
= AC - BC
= 27 - 12
= 15 m
We know that,
tan (θ) = opposite side / base side
Then, in △ ABE,
(Here, θ = missing angle)
tan (θ) = AB / BE
tan (θ) = 15/20
tan (θ) = 3/4
=》 θ = 37°
___________
Note:
Ray A & BE are parallel horizontal lines with AE as the transversal, so both the angles are equal to each other as then they will be alternate interior angles & they are represented in this question as 'θ'.
[Refer to the attachment for the figure]
____________________
Hope it helps ⚜
Related Questions
A college cafeteria pays student cashiers $7.70 per hour. Cashiers earn an additional $1.70
per hour for each hour worked over 35 hours per week. A cashier worked 41 hours one
week and 39 hours the second week. How much did this cashier earn in this two-week
period?
Answers
Answer:
$633
Step-by-step explanation:
Overtime:
(41 - 35 + 39 - 35) hours = 10 hours
Overtime rate: ($7.70 + $1.70)/hour = $9.40/hour
Regular time:
(35 + 35) hours = 70 hours
Regular rate: $7.70/hour
total pay = regular pay + overtime pay
total pay = $7.70/hour × 70 hours + $9.40/hour × 10 hours
total pay = $633
Find the volume of a right circular cone that has a height of 4.1 cm and a base with a diameter of 14.8 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answers
Answer:
[tex]V=235.1\ cm^3[/tex]
Step-by-step explanation:
Volume of a Cone
The volume of a right circular cone with height h and a base radius r is:
[tex]\displaystyle V=\frac{1}{3}\pi r^2 h[/tex]
The height of the given cone is h=4.1 cm and its diameter is d=14.8 cm. Since the radius is half the diameter, r=7.4 cm.
Calculate the volume:
[tex]\displaystyle V=\frac{1}{3}\pi\cdot 7.4^2\cdot 4.1[/tex]
[tex]\displaystyle V=\frac{1}{3}\pi\cdot 54.76\cdot 4.1[/tex]
[tex]\displaystyle V=\frac{1}{3}\pi\cdot 224.516[/tex]
[tex]\boxed{V=235.1\ cm^3}[/tex]
Darren and Jovanne are ata restaurant for dinner. They can choose their meal from three different cuisines Mexican (M). Greek (G) and American
A)
Which organized list represents all possible outcomes for Darren and Jovanne's dinner choices using the format of
(Darren's choice, Jovanne's choice)?
O (M,G),(M,A),(MM),(G,G),(G,A),(G,M),(A,G),(A,A),(A, M)
O (MG). (M,A),(G,A),(G,M),(A,G),(A,M)
O (M,G,A). (M,A,G),(G, M,A),(G, A, M). (A,G,M). (A,M,G)
O (MM). (G,G). (AA)
Answers
The sample space for their trial is given by:
(M,G),(M,A),(M,M),(G,G),(G,A),(G,M),(A,G),(A,A),(A, M).
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
In this problem, for each of the two people, there are three outcomes, hence the cardinality of the sample space is given by:
C = 2³ = 8.
Considering both can choose the same food, and each outcome has two options(Darren's and Jovanne's), the first option is correct.
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Think about a population mean that you may be interested in and propose a hypothesis test problem for this parameter. Gather appropriate data and post your problem, Later, respond to your own post with your own solution. For example, you may believe that the population mean number of times that adults go out for dinner each week is less than 1.5. Your data could be that you spoke with 7 people and found that they went out 2, 0, 1, 5, 0, 2, and 3 times last week. You then would choose to test this hypothesis at the .05 (or another) significance level. Assume a random sample.
Required:
Test this hypothesis at the 0.05 significance level.
Answers
Answer:
There is no sufficient evidence to conclude that population mean number of times that adults go out for dinner each week is less than 1.5
Step-by-step explanation:
From the question we are told that
The population mean is less than 1.5
The sample size is n = 7
The sample data is 2, 0, 1, 5, 0, 2, and 3
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{ \sum x_i }{ n }[/tex]
=> [tex]\= x = \frac{ 2 + 0 + 1 + 5 + 0 + 2 + 3 }{ 7 }[/tex]
=> [tex]\= x = 1.857 [/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ (2 - 1.857)^2 + (0 - 1.857)^2 +\cdots (3 - 1.857)^2}{7} }[/tex]
=> [tex]\sigma = 1.773[/tex]
The null hypothesis is [tex]H_o : \mu = 1.5[/tex]
The alternative hypothesis is [tex]H_a : \mu < 1.5[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]z = \frac{\= x - 1.857 }{ \frac{1.773 }{\sqrt{7} } }[/tex]
=>[tex]z = 0.53[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(z < 0.53 )[/tex]
From the z-table
[tex]P(z < 0.53 ) = 0.70194[/tex]
So
[tex]p-value = 0.70194[/tex]
From the values obtained we see that [tex]p-value > 0.05[/tex]
Here there is no sufficient evidence to conclude that population mean number of times that adults go out for dinner each week is less than 1.5
A family of 4 brothers is to be seated in a row at a theatre. How many seating arrangements are possible? Identify if the situation involves combinations or permutations
Answers
Answer:
its 24 permutations
Step-by-step explanation:
i just finished a test
There are 24 different ways 4 students can be arranged in a row.
What is permutation?A permutation in math is the number of ways in which a set of data or objects can be ordered or arranged, where the order matters.
Given that, a family of 4 brothers are to be seated in a row at a theatre,
We need to determine the order of the possible seating arrangements,
we conclude that there are =
1! x 2! x 3! x 4! = 24
different ways 4 students can be arranged in a row,
Hence, there are 24 different ways 4 students can be arranged in a row.
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Find the value of xxx, yyy, and zzz in the parallelogram below.
Answers
Answer:
Step-by-step explanation:
Write as an inequality: You have at least as many dogs as cats. (Someone please help me)
Answers
Answer:
d ≥ c
Step-by-step explanation:
Answer:
dogs ≥ cats
Step-by-step explanation:
A sheet of notebook paper is four thousandths of an inch thick. What is the thickness, in centimeters, of a 500-sheet stack of notebook paper
Answers
Answer:
2 inches thick
Step-by-step explanation:
4/1000*500
Thickness of a 500 sheet stack of notebook paper is 5 cm.
What is Measurement units?
A measurement unit is a standard quality used to express a physical quantity.
Given that;
Thickness of a sheet of notebook paper = 0.004 inch
Now,
1 inch = 2.54 cm
Hence, Thickness of a sheet of notebook paper = 0.004 inch
= 0.004 × 2.54 cm
= 0.01016 cm
= 0.01 cm
So, Thickness of a 500 sheet stack of notebook paper = 500 × 0.01
= 5 cm
Thus, Thickness of a 500-sheet stack of notebook paper is 5 cm.
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Which of the following would result in an integer?
a.) 110
b.) 92
c.) 100
d.) 60
Answers
Answer:
All choices are integers.
Step-by-step explanation:
All choices shown are integers.
Hello Can Someone Please Answer This Question I Will Mark You The Brainliest
Answers
I will tackle this problem by dividing the figure into 4 visible rectangles and 1 L shaped figure which i will add together to get the total area.
Rectangle (1)= h×w =4×5=20 cm²
Rectangle (2)= h×l =4×5=20 cm²
Rectangle (3)= h×l =4×5=20 cm²
Rectangle (4)= h×w =4×5=20 cm²
L-shaped polygon which i will divide into 2 parts
Part 1's area: l×w= 5×5=25 cm²
Part 2's area: l×w= 10×5=50 cm²
Total area=(20+20+20+20+25+50)
Total area=155 cm²
let their number of sides of a regular polygon is 6 in its radius is 5,then find the length of the side.
Answers
Step-by-step explanation:
area = n * a * ri / 2 , having ri - incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides) area = perimeter * ri / 2 , given ri and polygon perimeter.
please help me A portion of Taquan's check register is shown. Before Taquan made his utility payment on March 24, the balance of his account was $1,094.80.
Answers
The check register is used to show the total amount Taquan spent
Using the assumed values, Taquan's initial balance is $1336.26
How to determine the amount before making the utility payment?The question is incomplete, as the check register is not shown.
So, I will give a general explanation
Assume that the utility bill is $241.46
From the question, the new balance on March 24 is $1094.80
This means that the initial balance is:
Initial balance = New balance + Utility bill
This gives
Initial balance = $1094.80 + $241.46
Evaluate the sum
Initial balance = $1336.26
Using the assumed values, Taquan's initial balance is $1336.26
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What is the midpoint of AB?
Answers
A (-2,5) B ( 3,-3)
midpoint= ((-2+3)/2), ((5+(-3)/2)
= (0.5),(1)
Guys what is the definition of consecutive numbers? Anyone know? 20 points for first answer!!
Answers
They are integers that follow one right after another. For example the set {1,2,3,4,5} represents consecutive numbers. Another example would be {9,10,11,12,13}
In general, if x is some integer, then x+1 is the next integer right after x, and x+2 is right after x+1 and so on. The list is {x, x+1, x+2, x+3, ...} representing any general set of consecutive numbers.
Which expressions are polynomials?
Select each correct answer.
Answers
answer:35x^2
Step-by-step explanation:
the first one is not b/c its x/5
the second one is not b/c has a square root
the last one it has negative exponents
Answer:
Step-by-step explanation:
By definition, the power of each term in a polynomial must be greater than or equal to 0.
So x/5+2 is a polynomial
4x+sqrt(x)-1 is not because sqrt(x) is x^(1/2)
35x^2 is a polynomial
7x^7-x^(-5) is not because -5 is less than 0.
For every 15 bicycles seen in Harlem, there were 60 cars. How many cars will we need for 33 bicycles?
Answers
Answer:
132 bicycles
Step-by-step explanation:
The ratio of bicycles to cars is 15:60. Before anything, we need to simplify this ratio. 15/15 = 1, and 60/15 = 4. So, now we have 1:4. Since the question asks for 33 bicycles, we multiply the number of bicycles, 1, by 33. Since we are multiplying the bicycles, we also need to multiply the cars. 4 x 33 = 132.
33:132. We need 132 cars.
Question 15
7 pts
During a clothing store's Bargain Days, the regular price for T-shirts is discounted by $6. There is a state sales tax of 5%, and the $6 discount is applied before the
sales tax is calculated. A). Write an expression that shows the regular price r of a T-shirt minus the $6 discount. B). Write a rule for the function p(r) that expresses the
final price p of a T-shirt with the discount applied and sales tax added. C). How much would you pay during Bargain Days for a shirt regularly priced at $20.00?
Answers
Answer:
A) The expression that shows the regular price minus the discount is r - 6
B) The function is p(r) = 1.05r - 6.3
C) You would pay $14.7 during Bargain Days
Step-by-step explanation:
∵ The regular price is r
∵ The discount on it is 6%
∴ The price after the discount = r - 6
A) The expression that shows the regular price minus the discount is
r - 6
∵ The state sales tax is 5% applied after the discount
∴ The sales tax = 5%(r - 6)
→ Change 5% to decimal y dividing it by 100
∵ 5% = [tex]\frac{5}{100}[/tex] = 0.05
∴ The sales tax = 0.05(r - 6) = 0.05(r) - 0.05(6)
∴ The sales tax = 0.05r - 0.3
∵ p is the price of the T-shirt with discount and sales tax
→ Add the sales tax to the regular price minus the discount
∴ p(r) = r - 6 + 0.05r - 0.3
→ Add the like terms
∴ p(r) = (r + 0.05r) + (-6 - 0.3)
∴ p(r) = 1.05r + (-6.3)
∴ p(r) = 1.05r - 6.3
B) The function is p(r) = 1.05r - 6.3
∵ The regular price of a shirt is $20
→ Substitute r by 20 in the function above to find how much you would
pay during the Bargain Days
∴ p(20) = 1.05(20) - 6.3
∴ p(20) = 21 - 6.3
∴ p(20) = $14.7
C) You would pay $14.7 during Bargain Days
what is the area? please help. this would be my last question
Answers
Answer:
242
Step-by-step explanation:
Rectangle= 22*11= 242
Triangle= [tex]\frac{4*3}{2} =6[/tex]
242+6=
248
I need help on this question!
Answers
Sorry if wrong
Theo is driving with his mom to Paso Robles. It took Theo 4 hours to drive 228 miles. Lex drove with his dad to San Luis Obispo. Lex drove 186 miles in 3 hours. a. How far does Theo drive in 1 hour? How far does Lex drive in 1 hour? b. Who drove faster? Explain how you know.
Answers
Answer:
A. Theo drove 57 miles and Lex drove 62 miles in 1 hour.
B. Lex drove faster. We know this because in order to figure out how many miles each drove per hour you need to find there individual rate. Which is 228/4 and 186/3. You want to divide using the hours so you generate a response where 1 hour is the only thing left. Thus giving you mph (miles per hour). Lex is drove 5 miles more in an hour than Theo leading us back to who drove faster. Lex did.
Hope this helps!
slove for x
21/x = 6/8
Answers
Answer: x=28
Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
Answer:
x=21/68
I think that might be the answer
In a class, the ratio of the boys to the girls is 5:3. There are 15 girls in the class
8. Which of the following equation represents the ratio of the number of boys to the number of girls in the class?
A.5/3=×/15
B.5/3=15/×
C.5/15=3/×
D.3/5=×/15
9. How many boys are there in the class?
A. 10 boys
C. 20 boys
B. 15 boys
D. 25 boys
10. How many students are there in the class?
A. 30 students
C. 40 students
B. 35 students
D. 45 students
Answers
Answer:
ratio of girls to boy :5:3
Step-by-step explanation:
=5 x /8 x 100
x cancels x
Cary hiked 18 miles in 6 hours. If he continues at the same pace, how much farther can he hike in the next 2 hours?
Answers
Answer: I believe the answer is 6 miles.
Step-by-step explanation: Its states Cary hiked 18 miles in 6 hours. If you divide 18 by 6, you get the answer 3. This means that 6 multiplied by 3 will give you 18, so just do the same to the number 2. Two multiplied by 3 gives you 6.
a) (-2) + (-3) + (+2)=
b) (3) + (-3) + (-5)=
c) (1) + (8) + (-2)=
d) (5) + (-8) + (-1)=
e) (-6) + (-2) + (1)=
f) (-8) + (6) + (-2)=
g) (-7) + (6) + (-2)=
h) 6 + (-6) + (-7)=
i) -6 + (9) + (-4)=
j) (-4) + 2 + 4 + (1)=
Answers
Answer:
The answer is G and also your welcome
Step-by-step explanation:
Find the slope of line whose end points are (2,-5) and (4,-7)
Answers
Answer:
m = -1Step-by-step explanation:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(2,\:-5\right),\\\:\left(x_2,\:y_2\right)=\left(4,\:-7\right)\\\\m=\frac{-7-\left(-5\right)}{4-2}\\\\m = \frac{-7+5}{4-2}\\ \\m = \frac{-2}{2}\\ \\Simplify\\\\m =-1[/tex]
3. A warehouse holds 7,140 shoeboxes. Each aisle holds the same number of
boxes. How many aisles could there be?
a. 9
b. 4
c. 5
d. 6
4. A day care center has 66 children. Each teacher has the same number of
children. How many children could each teacher at the center have?
a. 9
b.4
c. 5
d. 6
5.630 employees work in an office building. The exact same number of employees
work on each floor. How many floors could the building have?
a. 6
b. 4
c. 10
d. 9
Answers
Answer:
1) b, c, d
2) d
3) a, c, d
Step-by-step explanation:
Just find the number that can divide by the whole. Say the question was
A pet shop have 20 pets. The same amount of pets are in each room. How many rroms could there be?
If there were 4 rooms, 5 pets would be in each. 20÷4=5. 4 goes into 20 so 4 could be an answer.
If there were 3 rooms, 6 rooms would have 3 pets and 2 would be left over. So it wouldn't work. You just need to find the number that goes into the whole with no remainder.
Your teacher asks the class to evaluate the expression (3³)¹. Your classmate gives an incorrect answer of 81. Evaluate the expression. Then find the likely error. **PLEASE FIND THE ERROR I DON'T NEED THE ANSWER I KNOW ITS 27**
Answers
Answer:
see explanation
Step-by-step explanation:
The most likely error is adding the exponents instead of multiplying them, that is
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then [tex](3^{3}) ^{1}[/tex] = [tex]3^{3(1)}[/tex] = 3³ = 27
However
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] ← the student may have used this definition to obtain 81
8 is greater than x, and 4 is less than or equal to x
Answers
Rude, we don't use such an answers here. Change it, please.
pls change it
hope.u understand
e. What is the value of 60 tens?
Answers
Answer:
The answer is 600
Step-by-step explanation:
Because 60×10=600.
Answer:
600
Step-by-step explanation:
60*10=600
I might have misunderstood. If I have, please tell me
A toy is marked up 25% from the original price, x.
Write two expressions to find the price of the
item after the discount.
Answers
Step-by-step explanation:
amount increased to the toy = y
new price of the toy after adding markup = z
y= ( ( 25/100) × X )
therefore z= x+y